Clyde produces chemicals. For anyc litres of chemicals he produces, he can sell allc litres at a per-litre market price pc=700. Clyde's cost of producingc litres of chemicals isCc(c)=5c2+100c Clyde wants to maximise his profit, given byc(c)=pccCc(c)=700c5c2100c

Bonnie is a baker, and can sell anyb loaves of bread she bakes at a per-loaf market price of pb=10. Bonnie is adversely affected by the noxious fumes emitted by Clyde's production of chemicals, so that her cost of bakingb loaves of bread depends on the litres of chemicalsc produced by Clyde, and is given by Cb(b,c)=21b2140b+bc. Bonnie wants to maximise her profitwhich now also depends on Clyde's output choice cand is given byb(b,c)=pbbCb(b,c)=10b21b2+140bbc.

(i) Derive the output of chemicals cthat maximises Clyde's profit c, by sloving forc in the first-order conditiondcdc(c)=0. Interpret Clyde's revenueRc(c)=pcc as his "benefit" from production, and sketch a graph that shows both Clyde's marginal benefit/revenuedcdRc(c) and his marginal cost dcdCc(c)as a function of c. Use your graph to briefly explain how the optimal outputc is determined.

(ii) Given any arbitraryc litres of chemicals produced by Clyde, find Bonnie's best-response output of bread b~(c), by solving forb in the first-order conditon bCb(b,c)=0. LettingRb(b)=pbb denote Bonnie's revenue/benefit from baking and selling bread, sketch a graph that shows both her marginal revenue dbdRb(b)and her marginal costbCb(b,c) as a function of b, for some arbitrary fixed valuec. Use your graph to briefly explain how Bonnie's best responseb~(c) is determined.

(iii) Now consider a situation where Clyde and Bonnie must simultaneously choose their outputsc and b, and solve for the Nash equilibrium(c,b) of the associated simultaneous-move game. Depict the best responses of both Clyde and Bonnie on a graph wherec is measured along the horizontal axis andb is measured along the vertical axis, and use your graph to explain how the Nash equilibrium(c,b) is determined.

Clyde produces chemicals. For any c litres of chemicals he produces, he can sell all c litres at a per-litre market price p = 700. Clyde's cost of producing c litres of chemicals is C'(c) = 5c2 + 100c. Clyde wants to maximise his profit, given by TT(c) = pec- Cc(c) = 700c - 5c2 - 100c. Bonnie is a baker, and can sell any b loaves of bread she bakes at a per-loaf market price of p = 10. Bonnie is adversely affected by the noxious fumes emitted by Clyde's production of chemicals, so that her cost of baking b loaves of bread depends on the litres of chemicals c produced by Clyde, and is given by C'(b, c) = 262 - 1406 + bc. Bonnie wants to maximise her profit-which now also depends on Clyde's output choice c-and is given by T (b, c) = pbb - Cb (b, c) = 106 - -62 + 1406 - bc. (i) [3 points] Derive the output of chemicals co that maximises Clyde's profit , by solving for c in the first-order condition -de do (c = 0. Interpret Clyde's revenue R"(c) = pc as his "benefit" from production, and sketch a graph that shows both Clyde's marginal benefit/revenue di ( and his marginal cost as a function of c. Use your graph to briefly explain how the optimal output co is determined. (ii) [3 points] Given any arbitrary c litres of chemicals produced by Clyde, find Bonnie's best-response output of bread b(c), by solving for b in the first-order condition on . = 0. Letting Rb (b) = pob denote Bonnie's revenue/benefit from baking and selling bread, sketch a graph that shows both her marginal revenue h @ and her marginal cost . as a function of b, for some arbitrary fixed value c. Use your graph to briefly explain how Bonnie's best response b(c) is determined. (iii) [4 points] Now consider a situation where Clyde and Bonnie must simultaneously choose their outputs c and b, and solve for the Nash equilibrium (co, b) of the associated simultaneous-move game. Depict the best responses of both Clyde and Bonnie on a graph where c is measured along the horizontal axis and b is measured along the vertical axis, and use your graph to explain how the Nash equilibrium (co, bo) is determined