Question

3. Consider the following Price and Quantity information for questions.

Price (P)	Quantity (Q)	Revenue	Marginal Revenue
20	0	0	-
18	4	72	18
16	8	128	14
14	12	168	10
12	16	192	6
10	20	200	2
8	24	192	-2
6	28	168	-6
4	32	128	-10
2	36	72	-14
0	40	0	-18

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

P = 20 – 0.5Q

(b) Write down the marginal revenue equation.

            P = 20 – Q

(The slope of MR is always twice greater (in absolute term) than the slope of demand. So if demand is P=a-bQ then MR=a-2bQ)

(c) Given that the total cost is 0.5Q², what would be the profit maximizing level of Q?

MR=MC. 20-Q=Q. So 2Q=20. Hence Q=10.

Profit Maximizing Level of Q = 10.

QUESTION:

Please explain and show steps to get to how MC=Q in this case

Answer 1

Answer : Given,

Total Cost (TC) = 0.5Q^2

Marginal Cost (MC) = TC / Q

This means that the marginal cost is the changes in total cost due to the changes in quantity. So,

MC = (0.5Q^2) / Q

=> MC = (0.5 * 2) * Q^(2-1) = 1 * Q^1

=> MC = Q

Thus, here MC =Q.