Question

1. Suppose that you have the following demand curve. Q  800  12P .01I
Q = quantity demanded P = price and I= average income.
You know that the current market price is $40 and average income is $40,000
i. Calculate current demand.
ii. Calculate the price elasticity of demand
iii. Calculate the income elasticity of demand
2. Assuming the unit price of a commodity is defined by: P = 90 – 2q, and the cost function is given as: C = 10 + 0.5 q 2 ,
i. Determine the profit-maximizing level of output and the unit price.
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ii. Determine the cost-minimizing level of output
3. Determine whether the following production functions show constant, increasing, or decreasing returns to scale:
i. Q = L 0.60 K 0.40
ii. Q = 5K 0.5 L 0.3
iii. Q = 4L + 2K
4. Given the cost function: C = 1000 + 10Q1/2 + Q + 2Q 2 , derive the average and marginal cost functions. At 5 units of output, what are the average and marginal costs.
5. A monopoly firm wishes to supply two different markets, 1 and 2, with the corresponding demand functions given as:
P1 = 500 – Q1 (Market 1)
P2 = 300 – Q2 (Market 2)
P1 and P2 represent the prices charged in markets 1 and 2, respectively, and Q1 and Q2 are quantities sold in markets 1 and 2, respectively.
The cost function is given by: C = 50,000 – 100Q
Find:
i. The profit maximizing output for the monopolist
ii. Allocation of output between the two markets
iii. The price charged in each of the two markets
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iv. The total or maximum profit.

Answer 1

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