EC229- Review session

EC229- Review session

Assume two cities, A and B, that can’t trade between them. Each city produces its own coconuts for its local market. If suddenly trade is possible then:

  1. Consumers from both cities are better off.
  2. Consumers from both cities are worse off.
  3. If consumers of city A are better off then so are the producers of city A.
  4. If consumers of city B are better off then so are the producers of city A.

D)

As we saw in class, the new price will be somewhere between the original price 𝑃_𝐴,𝑃_𝐵. Hence it

is impossible for consumers from both cities to be better off or worse off (since prices can’t exceed

𝑚𝑎𝑥(𝑃_𝐴,𝑃_𝐵) and can’t be below 𝑚𝑖𝑛(𝑃_𝐴,𝑃_𝐵). Therefore, answers a and b are false.

If the consumers of city B are better off this means they pay a lower price. If they pay a lower price it is because that the amount purchased has increased because of the possible trade. This means that the producers form city A are selling to consumers in city B, hence producers in city A are better off.

The iPhone’s market is less competitive as compared to Android’s. Which of the following values of elasticities and markups is most likely?

  1. iPhone’s demand elasticity is -2 and Android’s demand elasticity is -10. The markup for iPhone’s is 100% and for Android 11%.
  2. iPhone’s demand elasticity is -10 and Android’s demand elasticity is -2. The markup for iPhone’s is 100% and for Android 11%.
  3. iPhone’s demand elasticity is -2 and Android’s demand elasticity is -10. The markup for iPhone’s is

50% and for Android 20%.

  • iPhone’s demand elasticity is -10 and Android’s demand elasticity is -2. The markup for iPhone’s is

50% and for Android 10%.

a)

A less competitive market is less elastic (less negative) and a higher markup. In addition 𝑀𝐶 = 𝑃[1 + 1/𝐸𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦] so with elasticity of -2 the markup is 100% and with -10 it equals 11%.

Q3

If a monopoly produces a quantity such that the marginal revenue is 20 when the marginal cost is 10, it can increase profits by:

  1. Decreasing the amount produced, increasing the price per unit.
  2. Increasing the amount produced, decreasing the price per unit.
  3. Increasing the amount produced without changing the price.
  4. Decreasing the amount produced without changing the price.

B)

A monopoly can’t change the quantity supplied without affecting price, therefore answers c and d are false. If the MR is greater than the MC then producing another good is worthwhile (since the marginal revenue is greater than the marginal cost). Therefore, answer B is correct.

Q4

A monopoly produces a good at a marginal cost of MC(Q)=Q. The demand curve is given by P(Q)=16/Q+4. In this case:

  1. The equilibrium price is 8.
  2. The equilibrium price is 16
  3. The monopoly will not produce.
  4. The monopoly has positive profits only if it produces an amount Q>4.

A

Derive the MR: TR=P⋅Q=(16/Q+4)Q=16+4Q⇒MR=4

Equate MR=MC:    4=Q*

find the price: P*=16/Q* +4=16/4+4=8

Q5

GM sells its cars in Michigan through a dealer. Currently, GM quotes its dealers a price of $20,000 who sell the car to consumers at a price of

$27,000. Currently 50,00 cars are sold per year. GM considers vertical integration. Which of the following scenarios is more likely to occur upon integration?

  1. 60,000 cars will be sold at a price of $30,000.
  2. 40,000 cars will be sold at a price of $30,000.
  3. 60,000 cars will be sold at a price of $24,000.
  4. 40,000 cars will be sold at a price of \$24,000.

c)

Vertical integration leads to a higher quantity and lower retail price

Q6

A tourist is willing to pay 5 for a postcard. A local is willing to pay 1. Locals outnumber tourists 3:1. Assuming that it costs zero to produce one, what is the optimal price per postcard?

  1. 1
  2. 3
  3. 5
  4. It’s impossible to say.

C) Above 5$ no one buys. No use in pricing under 1$ or between 1$ and 5$ since 1$ and 5$ get the same number of buyers at a higher price.

At 1$ everyone buys and for every 4 people revenue is 4$.

At 5$, only 1 in 4 buys, but revenue is 5$.

Q7

You compete in a second-price auction for a painting. You value the painting at £500k and face only one other bidder. You do not know how her value but estimate it is uniformly distributed between £300k and

£700k. Your optimal bid is:

  1. Higher than £500K.
  2. Lower than £500k but not lower than £300k.

c) £500k

d) Impossible to tell without knowing what your opponent thinks about you.

c)-

In a second price auction it is optimal to bid your own value.

Q8

You compete in a first-price auction for a painting. You value the

painting at £500k and face only one other bidder. You do not know how

her value but estimate it is uniformly distributed between £300k and

£700k. Your optimal bid is:

  1. Higher than £500K.
  2. Lower than £500k but not lower than £300k.

c) £500k

d) Impossible to tell without knowing what your opponent thinks about you.

d) The optimal bid in a first price auction depends on the other bidder’s strategy.

Q9

The current exchange rate is 1.3 dollars to the British pound. The 1-year interest rate is 1% both in the US and in the UK. There are no bid-ask spreads or other transaction costs.

  1. There exists an arbitrage opportunity that involves buying the dollar using a forward contract if the forward rate is higher than 1.3.
  2. There exists an arbitrage opportunity that involves selling the dollar using a forward contract if the forward rate is higher than 1.3.
  3. The dollar is very likely to appreciate versus the pound next year.
  4. The pound/dollar exchange rate would very likely remain around 1.3 next year.

a) Given equal interest rates the forward rate equals the current exchange rate of 1.3. If the forward rate is higher then we should sell the pound forward or buy the dollar.

Q10

The current exchange rate is 1.3 dollars to the British pound. Next year, inflation will be 1% in the US and 2% in the UK.

  1. The dollar is very likely to appreciate versus the pound next year
  2. The pound dollar exchange rate would very likely remain around 1.3 next year.
  3. If the real exchange rate remains unchanged then the dollar will appreciate versus the pound in nominal terms.
  4. If the real exchange rate remains unchanged then the dollar will depreciate versus the pound in nominal terms.

c) Given the higher inflation rate in the UK for the real exchange to remain the same the pound will deprecate.

Q11

Assume that the exchange rate between the dollar and the GBP is 1 and that the federal reserve announces that in 1 year the exchange rate will be $1.2 per GBP. For the following interest rates decide which is not arbitrage free (i.e., for what interest rates it is possible to guarantee a positive profit). Explain your answer.

a)   rus=10%, rGB=10%

  • rus=20%, rGB=0%
  • rus=0%, rGB=20%
  1. If the interest rates are both 10% then it is possible to make a profit using the following method:

Borrow 100$. Convert them to pounds and invest in Britain. After one year you’ll have 110 pounds. Convert them to dollars and get 1.2⋅110=$132. Returning the borrowed $100+$10 interest leaves you with a net profit of $22.

  • If the American interest rate is 20% and the British interest rate is 0% it is not possible to make a profit. Converting a sum of $X to pounds will be worth, in terms of dollars:

X⋅(1+0)⋅1.2=$1.2X

Where (1+0) is the interest rate in Britain. This is the same as investing directly in the US.

  • It is possible to make a profit using the following method:

Borrow 100$. Convert them to pounds and invest in Britain. After one year you’ll have 120 pounds. Convert them to dollars and get 1.2⋅120=$144. Returning the borrowed $100+$0 interest leaves you with a net profit of $44.

Q12

Suppose that, in a perfectly competitive industry, every firm’s Total cost function: 𝑇𝐶(𝑄) = 5,000,000 + 4𝑄 + 𝑄2/50,000.

Demand is given by 𝐷(𝑝) = 375,000(42 − 𝑝).

  1. If the industry consists of five firms, with no possibility of entry or exit, how

much does each firm produce in equilibrium?

  • What is the profit of each firm?
  • How would you answer to part a) change if there would be a possibility of entry and/or exit? Provide a sketch of how one would solve for the equilibrium outcome
  1. The marginal cost for any one of the five firms is 𝑀𝐶

= 4 +     𝑄

25,000

,so at the price 𝑝, a firm supplies the solution to marginal cost equals price, or if we write the quantity sold as a function of price as 𝑠(𝑝) we get:

𝑠(𝑝)

4 +

25,00

= 𝑝 ⇒ 𝑠(𝑝) = 25,000(𝑝 − 4)

Of course, this is for prices 𝑝 above $4 only; for lower prices, each firm supplies zero. Since there are five such firms, industry supply

is five times this, or

𝑆        = 5 ⋅ 25,000                = 125,000(𝑝 − 4)

Market equilibrium is where supply equals demand, or

125,000(𝑝 − 4) = 375,000(42 − 𝑝) ⇒ 𝑝 − 4 = 3(42 − 𝑝) ⇒ 4𝑝 = 130

which is 𝑝 = $32.5 and each firm supply is given by:

𝑠              = 25,000

= 25,000

= 712,500

  • Based on prices and quantities that we calculated in part a) the total cost is 18,003,125 while total revenues for each firm equals 23,156,250. The profit for each firm is therefore 5,153,125
  • If there is free entry more firms enter the market so the profit will decrease from 5,153,125 to zero. Specifically, if we let the number of firms be N then the aggregate supply in the market is S(p,N)= N⋅25,000(p-4) and the equilibrium price is based on N⋅25,000(p-4)= 375,000(42 – p). This will give us p(N) and based on this we could calculate Q(N)=25,000(p(N)-4). Based on this we will be able to solve for the total cost and total revenues. The solution to N is based on equating the two. Since the number of firms is an integer, the solution is based on the highest integer lower than N
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