ECO204 Test 4.docx

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University of Toronto St. George
Kathleen Yuor Wong

--Lagrange Question:1)L (L,K,ƛ)=wL+rK- ƛ(function –q).2)Get 3 equation by derivative and chain rule and set =0.3)Set 1=2 by solving for ƛ.4)Solve for L and K without numbers, then plug back into equation 3. Then solve with numbers.5)To solve for P=MC=w/MPL. MPL=∂Q/∂L. --Single firm-Max Profit:1)Find R=P*Q.2)π =R–C.3)Solve for π and get FOC and set=0. 4)Solve for q and P. --DWL: Is the area between P.C. and monopoly or anything. --Consumer Surplus: Top part- is Below demand and above price. Producer S. is above supply and below price. --Decomposition Bundle: Keeps Utility constant and incorportes new prices. MUx/MUy=Px/Py --Income Effect: Is from decomp bundle to final. --Elasticities:1)Income-(Q -Q /I -I )*(I /Q ).2)ARC- (Q2-Q1)/(P2-P1)*(P1+P2/2)/(Q1+Q2/2). 2 1 2 1 1 1 --Risk Premium:1)Fine EU and EVariance.2)Then hold U constant and plug into given equation. Difference is risk premium. --T/F/U Help:1)For the firm to increase output in the short-run, it must increase their use of L. If the firm sees that MPL is decreasing, the statement is true. As the MPL decreases, it increases their MC and thus causes AC to increase as output increases. If the firm’s MPL is increasing, the statement is false. --In Perfect Competition: P=MC --In Cartel, Firms jointly behav2 as a Monopoly: To find max profit π1+π2=TR –TC = P*Q – AC*Q. We get π1+π2=4Q+9Q . Then find FOC ∂π/∂Q=0. Get big Q and determine q1 and q2. --Cournot Duopoly(Simultaneous revelation): To find Best Response functions- π1= P*q1 – AC*q1(or TCq ). Sub in equation for P and make big Q= q1+q2. Then π1=6q1-4q1 +5q1q2. 2 Then get FOC= ∂q1/∂q2. Then get BR function of q1=90+3q2. To solve for equilibrium plug in BR functions into each other. --Bertrand Duopoly: Behave as perfectly competitive sellers by competing on price. P=MC. This is if MC and AC same for both firms --Stackelberg Duopoly(Means one firm is moving first): FIRM TWO 2 moving first. To find Best Response functions- π1= P*q1–AC*q1. Sub in equation for P and make big Q= q1+q2. Then π1=6q1-4q1 +5q1q2. Then get FOC= ∂q1/∂q2. Then get BR function of q1=90+3q2. Then 2 take BR of firm 1 and plug into profit function of q2. Then π2= 7q2+ 8q2 . Then get FOC again and set equal to Zero and solve for q2. Then plug in q2 in q1 BR function and solve. --Derive FOC and firms Demand for Labor as a func
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