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