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Unformatted text preview: p Max: (Q) = TR - TC = QP(Q) - C(Q) how do we max (Q)? at the maximum profit: d( (Q))/ dQ = 0 Marginal Cost (MC(Q)) is dTR(Q)/dQ Marginal Revenue is MR(Q) dTC(Q)/dQ (Q) = TR(Q) - TC(Q) MR = MC Why MR = MC ? First Order Condition that dTR/dTC = 0 Suppose not: (1) If MR > MC, do a bit more activity, (2)If MR < MC, do a bit less, demand equation q = f(p) inverse demand equation p = f(q); p = f(q)* Q = TR (Q); MR = derivative of TR(q) Why derivative = 0 at local min and local max? Sufficient condition: 2nd derivative A change in fixed costs has no effect on the profit maximizing output or price. A change in total cost would cause the total cost curve to shift up by the amount of the change. There would be no effect on the total revenue curve or the shape of the total cost curve. Markup pricing (P - MC)/P = 1/ -Ep or P = (Ep/1 + Ep) MC Where MC equals marginal costs and Ep equals price elasticity of demand. Ep is a negative number. Therefore, -Ep is a positive number. the size of the markup is inversely related to the price elasticity of demand for a good. utility function is U(b,c)=b+100c-c 2 , where b is the number of silver bells in her garden and c is the number of cockle shells. She has 500 square feet in her garden to allocate between the two. Silver bells take up 1 square foot and cockle shells take up 4 square feet a. To maximize her utility, given the size of her garden, how many silver bells and cockle shells should Mary plant? a. To maximize U(b,c)=b+100c-c 2 subject to the constraint: b+4c<=500 . Plug b=500-4c into U(b,c) : U(c)=500 4c +100c - c 2 = 500 + 96c c 2 Take the derivative respect to c and set it to 0 (maximization): Plug 48 into b=500-4c : b = 308 If she suddenly acquires an extra 100 square feet for her garden, how much should she increase her planting of silver bells and cockle shells? Use the Lagrangian to solve this part. b.Now the constraint changes to: b+4c<=600. Objective function: U(b,c)=b+100c-c 2 Unit cost of...
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This note was uploaded on 12/16/2009 for the course SI 562 taught by Professor Chen during the Fall '08 term at University of Michigan.
- Fall '08