Refer to the table below: K L Y pY Cost Profit cars drivers output revenue wL +

Question

Refer to the table below: K L Y pY Cost Profit cars drivers output revenue wL + rK pY - wL - rK 1 1 2 1 3 1 1 2 2 2 3 3 Consider a company providing taxi rides to the airport. The inputs of production are drivers (L) and cars (K). The company can hire drivers at the going wage of w=30$ per day, and can also rent cars at the going rental rate of r=15$ per day. Suppose the production function is Cobb-Douglas, with productivity parameter A=10 and exponent on K equal to 1/3 and on L equal to 2/3 (so that they add up to 1). Interpret Y as the number of rides given by day. So to calculate the revenue you need to multiply by the price of each ride in dollars, which we assume to be 50. To calculate the MPL, use the expressions derived in class by taking partial derivatives. You can find them in the book and in the class slides. Recall that the cost of having K cars and L workers is given by: Cost=wL + rK. Fill the table above with the previous information and answer the following questions: What combination of drivers (L) and cars (K) yields the highest profits? (K,L) = (3,3) (K,L) = (3,2) (K,L) = (1,1) (K,L) = (1,3)

Explanation / Answer

K L Y MPL Revenue Cost Profit 3 3 30.00 6.67 1500.00 135.00 1365.00 3 2 22.86 7.62 1143.17 105.00 1038.17 1 1 10.00 6.67 500.00 45.00 455.00 1 3 20.88 4.64 1043.86 105.00 938.86 MPL = (20/3)*(K/L)^2/3 Profit is maximum at (K, L) = (3, 3)

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