In this module you learned that cost functions are derived from production functions and that the marginal cost curve is the inverse of the marginal product curve. Work through this problem to demonstrate those findings. Production Function: Total Product (Q) 1 3 6 10 15 Labor (L) 1 2 3 4 5 1. Using the production function, compute the figures for marginal product using the definition given earlier in this module. Draw a graph of the marginal product curve using the numbers you computed. Suppose this firm can hire workers at a wage rate of $10 per hour to work in its factory which has a rental cost of $100. Use the production function to derive the cost function. 2. First compute the variable cost for Q = 0 through Q = 5. 3. Next compute the fixed cost for Q = 0 through Q = 5. 4. Then compute the total cost for Q = 0 through Q = 5. This is the cost function. 5. Finally compute the marginal cost for Q = 0 through Q = 5. Draw the marginal cost curve and compare it to the marginal product curve above. Explain what you see

F MPI VC FC TC MC 0 100 100 1.00 10 100 110 10 0.50 30 100 130 20 6 0.33 50 100 160 30 10 0.25 100 100 200 40 15 0.20 150 100 250 50 Fixed costs are paid even if there is no output like rent which is 100 in our case and taken as fixed costs Variable costs are the labor costs which are calculated by the product of wages and labor MPL = Change in TP/Change in L, MC = Change in TC/Change in TP VC =10*L, FC =100 and TC = FC+VC As the MPI falls, the marginal costs go up 1.2 1 0.8 Marginal Product 0.6 0.4 0.2 0 0 2 4 6 10 12 14 16 Labor 60 50 40 Marginal Costs 30 20 10 0 0 2 3 4 5 6 Total Product/Output