1. Show whether the following production functions exhibit increasing, constant, or decreasing returns to scale.

a. Q = 2L + 3K b. Q = L + 5K + 10

c. Q = min (2*L, K)d. Q = 10*K*L

e. Q = L2 + K2 f. Q = K.5*L.5/2 + 10

2. Let the following combinations of capital and labor allow Acme Products to produce 10 Road Runner Traps. Find the cost of producing Q = 10 using each method if a) the wage is $10 and the price of capital is $20; b) the wage is $30 and the price of capital is $10.

Labor 1 2 3 6 12

Capital 10 5 3 2 1

3. Consider the following production function: Q = 4L + 10K.

a. Draw an isoquant diagram featuring the Q = 100 and Q = 200 isoquants (include numbers for L and K).

b. What is the marginal product of labor? Does this law of diminishing marginal product for labor apply to this production function?

c. Calculate the average product of labor when L = 10 and K = 10.

4. Let the production function for thingamajigs be Q = L1/2*K1/2 (this is the square root of L multiplied by the square root of K), the price of labor be $10 and the price of capital be $20. In the short run, the amount of capital is fixed at K = 100. Complete the following short run cost table for this firm (on your own paper, not this sheet!).

Quantity Labor Total Fixed Cost Average Fixed Cost Total Variable Cost Average Variable Cost Total Cost Average Total Cost

10

50

100

200

300

400

500

5. In each of the following cases, determine if Acme Products is minimizing cost.

a. Wage = $10, Price of Capital = $20, MPLabor = 3, MPCapital = 8;

b. Wage = $5, Price of Capital = $15, MPLabor = 2, MPCapital = 6;

c. Wage = $15, Price of Capital = $10, MPLabor = 6, MPCapital = 4;

d. Wage = $20, Price of Capital = $15, MPLabor = 6, MPCapital = 8;

6. On an isocost-isoquant diagram, draw the situation of a firm which is initially minimizing the cost of producing Q units of output. Then show how this firm’s cost-minimizing combination of capital and labor to produce Q changes when the wage of labor rises.

7. Consider the production function: Q = K*L. Let the wage of labor = $10 and the rental price of capital = $10. Determine the Q produced when L = 5 and K =5; when L =10 and K = 10; and L = 20 and K = 20. Draw the isoquant – isocost diagram showing these isoquants and combinations of K and L (which are cost minimizing given these prices, though if you cannot see why don’t worry and just take my word that they are). Determine the total cost and average cost for these three amounts of inputs and then draw an average cost with these three levels of Q. Verify that the average cost is indeed declining with Q, consistent with the increasing returns to scale for this production function.

8. Let a firm’s marginal cost curve be MC = 5 + Q/100.

a. Find the profit maximizing quantity if this firm is a price taker and faces a price of P = $12.

b. Find the profit maximizing quantity if this firm faces a marginal revenue curve of

MR = 15 – Q/100

9. Let the market demand curve for a good be: P = 50 – Q/10.

a. Recall that if the market demand curve is linear, the marginal revenue curve is also linear, with the same price-axis intercept and a slope equal to twice the slope of the demand curve. Write out the marginal revenue curve for this market demand curve.

b. The elasticity of demand can be written as (1/slope)*(P/Q). Find the elasticity of demand for this market demand curve at the following quantities: Q = 50, 150, 250, 350, 450.

c. Verify that the demand curve is elastic at quantities where marginal revenue is positive and inelastic at quantities where marginal revenue is negative.