Question

1. Assume that you are the economist for a coal mining company and have estimated the

demand curve facing your firm to be

?????

? = ?, ??? − ?????? + ????+. ???

where Png is the price of natural gas, which is assume to be $3/MMBtu and Pw is the price

of wind power, which is assumed to be $70/MWh.

A. What is the own price elasticity of demand when Pc = $80/ton? Is demand elastic or

inelastic at this price? What would happen to the firm's revenue if it decided to charge a

price below $80?

B. What is the own price elasticity of demand when Pcoal = $160. Is demand elastic or

inelastic at this price? What would happen to your firm’s revenue if it decided to charge a

price above $160?

C. What is the cross-price elasticity of demand between coal and natural gas at the original

prices in part a? Are coal and natural gas complements or substitutes? Answer the same

questions for wind, as well.

2.

Answer 1

Answer 1

(A)

Q_coal = 1200 - 5P_coal + 5*P_ng + 0.5*Pw

Given : P_ng = 3 and P_w = 70

Hence we have the following Demand :

Q_coal = 1200 - 5P_coal + 5*3 + 0.5*70

=> Q_coal = 1250 - 5P_coal

Elasticity of demand(e_d) = (dQ/dP)(P/Q)

When P = P_coal = 80 => Q = Q_coal = 1250 - 5*80 = 850 also ger dQ/dP = -5

Hence, e_d = (dQ/dP)(P/Q) = -5(80/850) = -0.47

Hence, own price elasticity of demand = - 0.47. As absolute value of elasticity of demand is lesser than 1 => Demand is inelastic

According to Total Expenditure method , If demand is inelastic and Price increases then Total revenue will also increase and if price decreases Total revenue will decrease.

As we have calculated above that demand is inelastic. Hence, Now if Price decreases Total revenue will decrease

(B)

When P = P_coal = 160 => Q = Q_coal = 1250 - 5*160 = 450

Hence, e_d = (dQ/dP)(P/Q) = -5(160/450) = -1.78

Hence, own price elasticity of demand = (-) 1.78. As absolute value of elasticity of demand is greater than 1 => Demand is elastic at P_coal = 160.

According to Total Expenditure method , If demand is elastic and Price increases then Total revenue will also decrease and if price decreases Total revenue will increase. Here demand is elastic. Hence Price goes above 160(i.e. increases) Total revenue will decrease

(C)

Q_coal = 1200 - 5P_coal + 5*P_ng + 0.5*Pw

Formula for Cross price elasticity between natural gas and coal is given by:

e_ng = (dQ_c/dP_ng)(P_ng/Q_c)

Q_coal = 1200 - 5*80 + 5*3 + 0.5*70 = 850 and P_ng = 3

=> e_ng = (5)(3/850) = 0.018.

As we can see that elasticity is positive i.e. as price of natural gas decreases demand of Coal will decrease and vice versa. Hence, we can say that Coal and wind power are substitutes

Formula:

e_w = (dQ/dP_w)(P_w/Q)

Q_coal = 1200 - 5*80 + 5*3 + 0.5*70 = 850

=> e_w = (0.5)(70/850) = 0.04

As we can see that elasticity is positive i.e. as price of wind power decreases demand of Coal will decrease and vice versa. Hence, we can say that Coal and wind power are substitutes