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Suppose the quantity of coffee supplied at every price decreases by 20 units. Furthermore you are told that the cross-price elasticity of doughnuts for coffee has a value of -1.0.

What is the new supply equation for coffee given the above information?
Calculate the new equilibrium price and quantity in the coffee market.
Using the simple percentage change formula (the standard mathematical definition of percentage change), what is the percentage change in the price of coffee given your answers in (c) and (e)?
Using the simple percentage change formula (the standard mathematical definition of percentage change), what is the percentage change in the quantity demanded of coffee given your answer in (c) and (e)?
Calculate the price elasticity of demand for coffee using two different methods: a) use the simple percentage change formula to get an estimate of the price elasticity of demand; and b) use the arc elasticity formula to get a numerical value of the price elasticity of demand.
Given your values in (g), is demand for coffee inelastic or elastic over this range of prices? Explain your answer.
Calculate the percentage change in the quantity of doughnuts demanded given this change in the supply of coffee. What will be the new quantity demanded of doughnuts?
Solutions;- 1) The supply curve will have the same slope but a different y-intercept than the original supply curve. The new supply equation will be Pc = b + (1/60)Qc. You need a point on the new supply curve so that you can use the coordinates of this point to find the new supply curves y-intercept. So, originally when Pc = $2 per cup, 60 units were supplied; now when Pc = $2 per cup, only 40 units are supplied-we can therefore use the coordinates (40, $2) in our equation in order to find the y-intercept. Thus, 2 = b + (1/60)(40) or b = 4/3. The new supply equation is Pc = 4/3 + (1/60)Qc. 2) 4/3 + (1/60)Qc = 5 (1/20)Qc (1/60 + 1/20)Qc = 5 4/3 (1/15)Qc = 11/3 Qc = 55 cups of coffee Pc = 5 (1/20)Qc = 5 (1/20)(55) = $2.25 per cup of coffee 3) Percentage change in the price of coffee = [(2.25 2)/2](100%) = 12.5% 4)Percentage change in the quantity demanded of coffee = [(55 60)/60](100%) = -8.3% 5)Price elasticity of demand for coffee = (% change in the…

y demanded of coffee)/(% change in the price of coffee) = 8.3%/12.5% = .664 Price elasticity of demand for coffee = [(Q2 Q1)/(Q2 + Q1)]/[(P2 P1)/(P2 + P1)]= (5/115)/(.25/4.25) .74 6) Demand is inelastic since the absolute value of the price elasticity of demand is less than one. 7)Cross-price elasticity of doughnuts for coffee = ( % change in quantity demanded of doughnuts)/(% change in the price of coffee) -1.0 = (% change in quantity demanded of doughnuts)/12.5% -12.5% = % change in the quantity demanded of doughnuts Quantity of doughnuts initially = 20 doughnuts Quantity of doughnuts now = (1 – .125)(20 doughnuts) = 17.5 doughnuts

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