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In: Economics

Based on the information below, answer questions (a)-(g) Price (P) Quantity (Q) Revenue Marginal Revenue 20...

Based on the information below, answer 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 down 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 a well-labeled graph that shows your answers from questions (a)-(f).

Expert Solution

(a) The demand equation would be , which represents a standard linear equation supposing that P is on vertical axis and Q on horizontal axis. For Q=0, we have , meaning that a=20. The b is slope as or or . Hence, the demand equation would be or .

Under statistical procedure, we would have , , , and . By the OLS method, we would have , and .

(b) The MR equation can be derived from the demand equation. The total revenue would be or or . The MR would be or or .

(c) The profit maximizing level would be where the MC is equal to the MR, ie where or or or units.

(d) The corresponding profit maximizing level of P would be or or dollars.

(e) The price elasticity would be or or or . At the profit maximizing level, the elasticity would be or or .

(f) The cost would be or or , supposing no fixed cost. The profit would be or . At the profit maximizing level, we have or or or dollars.

(g) The graph and table would be as below. Note that .

P	Q	TR	MR
20	0	0	-
18	2	36	18
16	4	64	14
14	6	84	10
12	8	96	6
10	10	100	2
8	12	96	-2
6	14	84	-6
4	16	64	-10
2	18	36	-14
0	20	0	-18

Rahul Sunny answered 2 years ago

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