Micro economic question

Levin. There used to be a rule of thumb in the gasoline industry that each 10 cent increase in the price of gas adds sio billion to industry revenues. We can write this rule of thumb as dTR 0.10 = 10 dp (a) Recall that TR= pQ, and assume price is fixed. Show that the derivative TA can be expressed in elasticity form as dTR = Q(1 +e) dp Prove that for inelastic demand. TR rises when prises. (b) Now suppose you also know that the market quantity of gas consumed is Q = 130. Show that you can obtain an elasticity estimate ofe= -0.23 from the rule of thumb and the deriva- tive in part (a). (c) Let the demand of a typical consumer for gas be 40p)= Amp Suppose you know that the typical consumer buys 4 = 700 gallons of gas per year at a price of p – 2.50 per gallon. You also know that the typical consumer has an income of m= 50,000, and you know the elasticity estimate from part (b). If you do a back of the envelope calculation to calibrate the demand curve, what values do you get for A and bf (d) What is the income elasticity of demand for gas? Use your de mand function from part (c) and continue to assume we are at the point p = 2.50, 4 – 700, m = 50000. Using the words normal good, necessity, and luxury, explain whether you think this is a good estimate of the income elasticity of demand for gas.

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