Question

[10 points] Suppose the market demand and market supply curves for coffee are given by the following equations where P is the price per cup of coffee and Qc is the quantity of billion cups of coffee: Market Demand for Coffee: QD = 120 – 6P Market Supply of Coffee: Qs = -10 + 20P a. [2 points) What is the equilibrium price and equilibrium of coffee given the above information? Suppose the quantity of coffee supplied at every price decreases by 13 units. Furthermore you are told that the cross-price elasticity of doughnuts for coffee has a value of -2. Use the information to answer b-e below. b. [2 points] What is the new supply equation for coffee given the above information? c. [2 points] Calculate the new equilibrium price and quantity in the coffee market. d. [2 points] What is the percentage change in the price of coffee given your answers in (a) and (c)? e. [2 points] Calculate the percentage change in the quantity of doughnuts demanded given this change in the supply of coffee.

Answer 1

At equilibrium cod - 120-6p = -10 + 20 p ( 120 + 10) =(20p + 6p) 130 = 26p P = (130/26) 1P 5 (Eguilibrium price of coffee) and, Q = 120-6p a = 120-665) 90 e (Ejuh brim guantity of coffee). 6 quantity of coffee supplied at every price decrease by 13 units New Supply function of lotzop -13 10 = -23 + 20p O At new equilibrium, ad co} = d. // 120 - 6p) = -23 720p (120 +23) = zopt op 143 = 26 p P2 (143/26) P = 5.5 (New equilibrium price of coffee) and @= 120-6p a 120-6(55) 10 287 (New equilibrum guantity of coffee

Price of coffee increaded from 5 to 5.5. /- change in price of coffee (5.5- 5 0 I change in price of coffee = 10 o change in supply of coffee load to change the price of ciftes by lo of Crow price elasting of dagnits for coffee of change in city of doughts 7. change in price of coffee -2 t change in city of dougnett - 7 change in aty of douugnuto = (-2) (10) 7. change in aty if doughts = -20 - There would be 200% decreak in gty of deughts.

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