22. Suppose a firms inverse demand function is as follows: P= 40 - Q/2 A) What i

Question

22. Suppose a firms inverse demand function is as follows: P= 40 - Q/2

A) What is the firms total revenue function?

B) What is the firms marginal revenue function?

C) At what quantity is the firms total revenue maximized?

D) What is the price paid by consumers at the quantity where the firms total revenue is maximized?

E) At the price $30, what is the firms price elasticity of demand in absolute value?

F) At the price of $30, is the demand elastic, unit elastic, or inelastic?

23. P= 10 – Q/5 and P= Q/10 – ½

A) Determine the equilibrium price and quantity.

B) Graph the inverse demand and supply curve with Q on the horizontal and P on the vertical axis. Clearly label all axis and curves, and identify the equilibrium price and quantity.

Explanation / Answer

22.

P= 40 - Q/2 is the inverse demand function also the demand function can be rewritten as

Q/2 = 40-P or Q = 80 - 2P

The total revenue functon can be calculated by multiplying the inverse demand function by Q.

TR= 40Q - Q^2/2

MR or the marginal revenue is the first order derivative of the total revenue or the TR function.

MR = dTR/dQ = 40-Q

to max TR we take dTR/dQ = 0

dTR/dQ= 40 - Q = 0 or Q = 40

that means that TR or total revenue is maximised at Q=40 units

at Q=40, P = 40-40/2 = 20

at P=30, Q = 80-2*30 = 20

Ed at P=30 = dQ/dP*(P/Q) = -2*(30/20) =-3 The demand is greater than 1 which means it is ELASTIC

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