# Calculate price elasticity and explain step by step

Suppose the demand function is Q=100-P, where Q is the quantity demand and P is the price. Please calculate the price elasticity at P=10 (by comparing it with a pair of price and quantity at P=20). Calculate the change in total revenue which is P times Q moving from P=10 to P=20. Repeat the same exercise for P=70 versus P=80.

please provide step by step.

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#### Solution Preview

(a) Q0 = 100 - P0 = 100 - 10 = 90, Q1 = 100 - P1 = 100 - 20 = 80

Price Elasticity of demand =|[2(Q1 - Q0)/(Q1 + Q0)] / [2(P1 - P0)/(P1 + P0)]|

= |[2(80 - 90)/(80 + 90)] / ...

#### Solution Summary

A Complete, Neat and Step-by-step Solution is provided.

Managerial Economics

You are the manager of a monopoly, and your demand and cost functions are given by

2

P=200-2Q and C(Q)=2,000+3Q , respectively.

a. What price-quantity combination maximizes your firm's profits?

b. Calculate the maximum profits

c. Is demand elastic, inelastic, or unit elastic at the profit-maximizing price-quantity combination?

d. What price-quantity combination maximizes revenue?

e. Calculate the maximum revenues.

f. Is demand elastic, inelastic, or unit elastic at the revenue-maximizing price-quantity combination?

You are the manager of a firm that produces a product according to the cost function

2 3

C(qi ) = 100 +50qi - 4q i + qi . Determine the short-run supply function if:

a. You operate a perfectly competitive business.

b. You operate a monopoly.

c. You operate a monopolistically competitive business.