# 1. Assume that you are the eco

1. Assume that you are the economist for a coal mining companyand 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 revenueif 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’srevenue if it decided to charge a

price above $160?

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

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

questions for wind, as well.

2.

Answer:

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 absolutevalue of elasticity of demand is lesser than 1 => Demand isinelastic

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

As we have calculated above that demand is inelastic. Hence, Nowif 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 absolutevalue of elasticity of demand is greater than 1 => Demand iselastic at P_{coal} = 160.

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

(C)

Q_{coal} = 1200 – 5P_{coal} + 5*P_{ng} +0.5*Pw

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

e_{ng} =(dQ_{c}/dP_{ng})(P_{ng}/Q_{c})

Q_{coal} = 1200 – 5*80 + 5*3 + 0.5*70 = 850 andP_{ng} = 3

=> e_{ng} = (5)(3/850) = 0.018.

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