Question

1. Given the table below, compute total product for resources A and resources B Both resources are varible and are employed in purely competitive markets. The price of A is $4.00 and the price of 8 is $8.00. The Final product is $1.00 per unit. (20 points) Quantity of Resources A Quantity of resources B Marginal Product of B TP MRP TRB Marginal TRA Employed Product of A TP MRP 40 32 24 20 16 36 32 24 16 12 5 Compute total product, and MRP A. What is the least-cost combination of resources A and B that would enable the firm to produce 312 units of output? B. What is the profit maximizing combination of A and B? C. What is the total output and profit when the firm is employed the profit maximizing combination of A and B?

Answer 1

A) There is only one combination of A and B that makes a total output of 312 and this is when 7 units of A and 7 units of B are employed. TP is 144 + 168 = 312. The cost incurred is 7*4 + 7*8 = $84

B) Profit is maximized when A and B are hired according to MRP = price of input rule

Since price of A is 4, we must hire 7 units of A as its MRP is 4. Similarly, price of B is 8, we must hire 8 units of B as its MRP is 8. Hence profit maximization bundle is same as cost minimization for 312 units

Profit = 312*1 - 84 = 228

C) Total output is 312 units. Profit = TRA + TRB - TC = 144 + 168 - (7*4 + 7*8) = 228

Note: MRP = MP * price of final output

TP = cumulative sum of marginal product

TRA or TRB = total revenue from A or B = TP * price of final good.

TRA	Quantity of resources A	MP of A	TP	MRP	Quantity of resources B	MP of B	TP	MRP	TRB
40	1	40	40	40	1	40	40	40	40
72	2	32	72	32	2	36	76	36	76
96	3	24	96	24	3	32	108	32	108
116	4	20	116	20	4	24	132	24	132
132	5	16	132	16	5	16	148	16	148
140	6	8	140	8	6	12	160	12	160
144	7	4	144	4	7	8	168	8	168