Question

3. Estimate Supply

a. Suppose you are given this information from a movie theater making rational, optimized decisions. Sketch a graph of supply (total cost and quantity) for “theater movies” using the available data.

Price of Price of Number Theater Theater Output Workers Film per Worker Quantity (Movies per Hour 1000 ft Hours of Film Produced)Labor) Capital) UsedUsed 15 18 13 20 100 120 80 95 1.0 1.5 3.0 5.0 0.2 0.3 0.6 1.5 8

b. Estimate the quadratic cost function (i.e., ??? = ? + ???? 2 ) for “theater movies” that best approximates the data and add it to your graph

c. What are the average and marginal cost equations based on your estimate? Is there a non-zero quantity that minimizes these unit cost measures?

Answer 1

In this analysis, the objective is to estimate the supply schedule using the information on the quantity supplied (qTM) and labor & capital cost involved.

The total cost (CTM) is given by: Labor cost + Capital Cost

Thus, for 2 movies, the labor cost is 15*1=15 and capital cost is 100. Hence, for producing 2 movies, the total cost is 115

Similarly, for 3 movies, the labor cost is 18*1.5=27 and capital cost is 120. Hence, for producing 3 movie, the total cost is 147

Thus, supply schedule (qTM versus CTM) is:

qTM	CTM
2	115
3	147
5	119
8	195

3a) On plotting the supply schedule, the result is:

3b) On estimating the quadratic cost function in excel, the result is:

Thus, the quadratic cost function is:

3c) The average cost equation is given by:

The marginal cost function is given by:

It shall be observed that it is at zero quantity only that the marginal cost is zero. At every positive quantity, the marginal cost function shows an increasing trend. Hence, for marginal cost, there is not any non-zero quantity that minimizes the marginal cost.

On the other hand, the minimum value of average cost is obtained when qTM=sqrt(114.6698241/1.150202977)=9.984753 and that minimum value of average cost is 22.96898544

Thus, there is non-zero quantity at which the average cost is minimum.