Question

Part 2 of: The demand for good X is estimated to be: Qx = 800 - 40Px - 25Py + 0.5M + 12Ax

Parts A-G already answered

h. Produce a graph of total revenue and marginal revenue. Graph total revenue for quantities up to 2,500 and put the marginal revenue graph on separate axes, and graph marginal revenue for quantities up to 2,500 also. i. What level of sales will maximize the company’s total revenues? What price does the company have to charge for X for that level of sales result?

Answer 1

TR = PQ = PXQX.

Find inverse demand function PX = 2460/40 – QX/40

PX = 61.5 – 0.025QX

TR = (61.5 – 0.025QX)QX

MR = 61.5 – 0.05QX

h. Total revenue and marginal revenue are plotted below for QX up to 2,500.

i. The level of sales that will maximize the company’s total revenues is the one that makes marginal revenue 0

MR = 0

61.5 – 0.05QX = 0

QX = 1230

Hence the quantity 1230 will maximize revenue.

Price = 61.5 – 0.025*1230 = 30.75 is the required price.

Required table

Q	Total revenue	Marginal revenue
0	0	61.5
500	24500	36.5
1000	36500	11.5
1500	36000	-13.5
2000	23000	-38.5
2500	-2500	-63.5