Question 1 (15%)
Given the data below, make an appropriate forecast for the following year:
- using a 3-period moving average
- using a naive forecast for period 6
- using an exponential smoothing (an alpha of 0.4 and period 1 as the initial forecast)
- using a linear trend line
Question 2 (15%)
ABC company has recorded the following sales (000 omitted).
- Compute 2005 sales, using the method of least squares
- Compute the coefficient of determination
- Comment on the reliability of the estimated sales equation, together with the necessary assumptions if the estimated equation is to be used to predict sales.
Question 3 (15%)
A film processor company has the following production function:
Q = 0.5K2 + 0.3KL + 0.4L2
Assume a weekly rate of use where L = 110 labor hours and K = 40 film developing hours. Determine the following:
- The total product per week.
- The marginal product of labor.
- The marginal product of capital.
Question 4 (10%)
A company has developed the following production function for its coal output:
Q – 250L0.5K0.6
- Determine return to scale, and comment on it.
- Determine returns to scale for each factor input.
Question 5 (15%)
The total product of labor (per hour) for a firm is given by:
Q = 30L – 0.5L2
- Determine the marginal product of labor.
- How many workers should the firm employ if the wage rate is $30 per hour and the marginal revenue product is $24.
Question 6 (15%)
Given the cost function for your firm: TC = 30 +3Q +2Q2
- What is the average fixed cost (AFC) of producing 5 units of output?
- What is the average variable cost (AVC) of producing 5 units of output?
- What are the average total cost (ATC) and marginal cost (MC) of producing 5 units of output?
Question 7 (15%)
Given the following total cost (TC) function:
TC = 100 + 70Q – 1.5Q2 + 0.01Q3
- Calculate the marginal cost (MC), average variable cost (AVC), average cost (AC), and average fixed cost (AFC) functions.
- At what level of output does MC reach its minimum? AVC? AFC?
- Determine MC and AVC when AVC is at its minimum.
- Prove that short-run MC equals AVC when AVC is at its minimum.
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