Question

3. [Individual and Market Demand](15%) Suppose the domestic demand for oil in the US is Qpp = 1000-30P, and the foreign demand is QFD = 1400-50P, where the quantity demanded is measured in gallons and price is in dollars per gallon. 4. [Utility Maximization](25%) Mary spends her income on housing (H) and food (F). Her utility function is given by: U(H,F) = 3HF-H+F a) (5%) What is the equation(s) for the world demand of oil? Please draw the domestic demand, foreign demand and world demand in a figure. Suppose the price of food is $1 per unit and the price of housing is $2 per unit. Assume her income is $9. a) (5%) Write down Mary's budget constraint and find the expression for her marginal rate of substitution (MRSHF). b) (5%) Suppose the world supply of oil is given by Qs = 600 + 40P. The world equilibrium price of oil is $ per gallon and the equilibrium quantity of oil is g allons. b) (5%) Assume the optimal choice of (HⓇ,F*) is not a corner solution. Write the equation that represents the tangency between Mary's budget constraint and her indifference curve. c) (5%) Suppose there is price control on oil. Assume the world oil price is $10 per gallon. What is the quantity demand and quantity supply of oil? Is there an excess supply or a shortage or oil? c) (5%) Find the optimal quantity of housing (HⓇ) and all other goods (F*).

Answer 1

3) INDIVIDUAL AND MARKET DEMAND DOMESTIC DEMAND FOR OIL IN US,QOD = 1000-300 FOREIGN OUMANO FOR OIL ; QFD=1400 -5P QUANTITY DEMANDED MEASURED IN GALLONS PRICE IS IN COLLARS PER GALLON (a) WORLD DEMAND = POMESTIC DEMAND+ FOREIGN DEMAND Qo = Qoot Q FO Qo= 1000- 30f)+ (1400 - 5p) QO = 2400-80p PRICE -> QRA COOMESTIC DEMAND) QpCWORLD DEMAND 28 QFO (FOREIGN DEMAND > QUANTITY 1000 1400 Scared with CamScanner

(b) WORLD WORLD SUPPLY, OF OIL, Qs = 600+40p AT EQUILIBRIUM, WORLD DEMAND = WORLD SUPPLY QO = QS 2400 -80P= 600 + 40P =) 2400 - 600 = 40P+ 80P 1800 = 1200 =) p = 1800 -15 120 EQUILIBRIUM PRICE OF ONE GALLON OF OIL is $15 QO= 2400-80P=2900 - 80(15) = 1200 GALLONS - Qs = 600 +40 P = 600 + 40(15)=1200 GALLONS EQUILIBRIUM QUANTITY is 1200 GALLONS OF OIL co) PRICE CONTROL IS IMPOSED ON OIL AT $10 PER GALLON WORLD DEMAND FOR OIL AT PRICE $10 PER GALLON, PO = 2400 - 80P = 2400 - 80010) = 1600 GALLOWS WORLD SUPPLY FOR OIL AT PRICE $10 PER GALLON, QS = 600 +40P = 600 +40(10)= 1000 GALLONS WORLD O EMAND EXCEEDS WORLD SUPPLY THERE IS EXCESS DEMAND IN WORLD OIL MARKET EFORE, THERE IS SHORTAGE OF OIL Scanned with CamScanner I THEREFORE, THERE

LITY MAXIMIZATTON UTILITY FUNCTI "Y FUNCTION OF MARY, OCH, F=3HF - H+ H = HOUSING F- FOOD PF = PRICE OF FOOD=$1 PER UNIT H-PRICE OF HOUSING = $2 PER UM M=INCOME OF MARY = $9 SINCE MARY SPEN a BUDGET CONSTRAINT FOR MARY E MARY SPENDS HER INCOME ON HOUSING AND FOOD . PEF + PM = M BOVE EQUATION IS BUDGET CONSTRAINT WE HAVE TO FIND MARGINAL RATE OF SUBTITUTION TO MRSHE IS RATE AT WHICH MARY IS WILLING SACRIFICEE HOUSING UNITS OF HOUSING TO GAIN UNITS OF FOOD MRSHE = OF. MUH JUCH,F) AH IF TH MUC GUCH, FVOF MUM = MARGINAL UTILITY OF HOUSING MUE=MARGINAL UTILITY OF FOOD MOMS QUCIT, F) 3F - My = DICH F2 3H+1 әИ Р MRSMES MUH, 35-) 3H+ OF CH*F*) IS NOT (6) AssumiNG OPTIMAL CHOICE COR CORNER SOLUTION cs Scanned with CamScanner

EQUATION FOR - CONSTRAINT AND ? SLOPE OF INDIF TON FOR TANGENCY BETWEEN MARY'S BUDGET AINT AND HER, INDIFFERENCE CURVE E OF INDIFFERENCE CURVE SLOPE OF BUDGET CONSTRAINT =) MRSHF = Pu MRSHE = SLOPE OF INDIFFERENCE CURVE ē - PRICE RATIO - SLOp OF BUDGET CONSTRAINT C) OPTIMAL QUANTITY OF HOUSING CH*) AND FOOD CF*) CAN BE FOUND BY EQUATING : MRS & PRICE RATIO RATIO - MRS HE = P4 = 3 F -) 3F-1 - 2 314+1 T 3F -1=2(3H+1) 3f-1cH+2 - BF-6H=3 =) 3(F-2H2=3 - Ifr2H) - 1 - F= 2H+) NOW, PEF + PHH =M = F + 2H -9 cs Scamped w211 +1+2H = 9 Cand canner

- 4H + 1 = $ => 4H=8 H=2 OPTIMAL NUMBER OF HOUSING IS 2 UNITS FS 2H+) = 22)+1= 5 UTILITY ATTAINED BY QUANTITY OF HOUSING AND CONSOMING OPTIMAL FOOD, UCH* p*} UCH7 F*)= 3HF - HUF = 3(2)5)-2+5 ~ 30 -2+5 = 33 CS Scanned with CamScanner