Econ 331 PS1 I) Suppose that the quantity of steel demanded in France is given b
ID: 1138238 • Letter: E
Question
Econ 331 PS1 I) Suppose that the quantity of steel demanded in France is given by Qa 100-2P+0.5Y+0.2PAa where Qs is the quantity of steel demanded per year, P is the market price of steel, Y is real GDP in France, and Pa is the market price of aluminum. In 2011, market conditions are such that P-10, Y-40, and P,-100. a) How much steel will be demanded in 2011? b) What is the price elasticity of demand, given market conditions in 2011? Is Demand elastic, inelastic or unitary elastic? Based on the value that you calculate, give a sentence that explains the value. Give an appropriate sentence that explains this value. For this elasticity measure, it should begin with "If price increases by 1%, " c) What is the income elasticity of demand, given market conditions in 2011? Give an appropriate sentence that explains this value. d) What is the cross-price elasticity of demand for steel with respect to aluminum, given market conditions in 2011? Give an appropriate sentence that explains this value. e) If price of steel is not set at 10 but Y and PA remain fixed at their values of 40 and 100, what is the equation for demand? What is the market's choke price?Explanation / Answer
c) The income elasticity of demand is given by :
E(income) = (dQ/Q * 100) / (dY/Y * 100) = dQ/dY * Y/Q (1)
Differentiating the given demand equation with respect to Y , we get,
dQ/dY = 0.5
Substituting P=10, PA = 100 and Y= 40 into the demand function, we get,
Q = 100 - 20 +20 +20 = 120
Therefore, elasticity of demand (from (1)) = 0.5 * 40/120 = 1/6 = 0.166
This value shows that when income changes by 1%, the quantity of steel demanded increases by 0.166%.
d) The cross price elasticity of steel with respect to aluminium is given by dQ/ dPA * PA/Q
Differentiating the demand function with respect to PA, we get dQ/ dPA = 0.2
Cross price elasticity = 0.2 * 100/120 = 0.166
This value shows that for every 1% increase in the price of aluminium, the quantity demanded of steel increases by 0.166%.
e) When the price of steel is not fixed at 10, but the price of aluminium is fixed at 10 and the income is fixed at 40, we can substitute the values Y=40 and PA = 100 in the demand equation to get,
Q = 100 - 2P + 0.5*40 + 0.2* 100
Q = 100 -2P + 20 + 20 = 140 - 2P
Therefore the demand equation is Q = 140 - 2P.
Choke price is the price at which the quantity demanded becomes zero. So, substituting Q =0 in the demand function, we get,
0 = 140 - 2P or P = 70
Therefore the choke price of steel is 70.
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