1. Numerical Problem 1: Understanding Elasticities (5 pt) Suppose the demand cur
ID: 1147522 • Letter: 1
Question
1. Numerical Problem 1: Understanding Elasticities (5 pt) Suppose the demand curve for a product is given by Q = 10-224 0.25Ps, where P is the price of the product and Ps is the price of a substitute good. The price of the substitute good is $2.00. Suppose P = $1.00. a) What is the price elasticity of demand? How do you interpret this value in economic sense? (3 pt) b) What is the cross-price elasticity of demand? How do you interpret this value in economic sense? (Hint: refer to the lecture slides, use the cross-price elasticity of demand formula. The marginal effect of price of substitute good on demand a 0.25.) (2 pt)Explanation / Answer
Q=10-2P+0.25Ps From here we can get dQ/dP=-2 and dQ/dPs=0.25
Q=10-2(1)+0.25(2)=8+0.5=8.5
1) price elasticity of demand=dQ/dP*(P/Q)= -2*(1/8.5)=-0.2352
It means when price of a commodity increases by 1% then quantity demanded of a commodity decreases by 0.23%, cetris paribus.
2) Cross price elasticity=dQ/dPs*(Ps/Q)=0.25*2/8.5=0.0588
Cross price elaaticity implies if price of substitue good increases by 1% then quantity demand of a good increases by 0.0588% keeping price and other factor constant and thus makes 2goods as substitute because cross elasticity is positive.
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