Question

Based on the information below, answer the questions (a)-(g)

Price (P)	Quantity (Q)	Revenue	Marginal Revenue
20	0
18	2
16	4
14	6
12	8
10	10
8	12
6	14
4	16
2	18
0	20

(a) Based on the information above, write down the demand equation.

(b) Write the marginal revenue equation.

(c) Given that the marginal cost is Q, what would be the profit-maximizing level of Q?

(d) What would be the profit-maximizing level of P?

(e) What would be the price elasticity at the profit-maximizing P?

(f) What would be the maximized profit?

(g) Draw graphs that show your answers from questions (a)-(f).

Answer 1

a. When P=0, Q=20 and when Q=0,P=20

This means that the demand curve has a vertical intercept and a horizontal intercept of 20 each.

Slope of the demand curve = - vertical intercept/horizontal intercept = 20/20 = -1 (negative sign indicates that the demand curve is downward sloping)

Thus, equation of the demand curve with a horizontal intercept of 20 and a slope of -1 is Q=20-P.

b. From a, inverse demand function can be written as P=20-Q

Then, TR = P*Q = 20Q-Q²

Now, MR = dTR/dQ = 20-2Q

c. If MC=Q, then, equilibrium condition for profit maximization requires MR=MC

or, 20-2Q=Q

or, 3Q = 20

or, Q = 20/3 = 6.67

Thus, the profit maximizing level of Q is 6. (from the table)

d. At the profit maximizing level, P=$14 (from the table)

e. Price elasticity at the profit maximizing level of P = P/Q * dQ/dP

or, e = 14/6 * d(20-P)dP

or, e = 14/6 * (-1) = - 2.33

f. Maximized profit = TR - TC = 20Q-Q² - 6Q = 14Q-Q²

At Q=6. Profit = 14*6 - 6² = $48

g. The required diagram from the information obtained above is shown below:

Price $20 $14 Prof MC Q 6 $6 Demand Quantity 20 6 MR