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  3. 3 consider a monopolist whose total costs are given by...

Question: 3 consider a monopolist whose total costs are given by...

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3. Consider a monopolist whose total costs are given by C(y)竺kv2 and who faces the demand curve y-a-bp , where y > O įs the rate of output of the monopolist and p>0 įs the price it receives for its output. (a) What restrictions on the values of the parameters (a,b,k) would you be inclined to as- sert, a priori? Explain your restrictions in economic terms. (b) Assume the monopolist faces a tax per unit of output, say t>0. Set up the profit maxi- mization problem faced by the monopolist. You are to use output as the decision varia- ble. This means that you will have to solve for the invefse demand curve in order to for mulate the correct profit maximization problem. (c) Derive the FONC and SOSC. Find the profit-maximizing value of output and denote it (d) Confirm , output falls as the unit tax (e) What restriction does the SOSC impose on (a.b,k)? Is this restriction weaker or strong- by y-y(a,b,k,t) that for the restrictions placed on (a.b,k) in part (a) rises. er than your a priori restrictions? (f) Substitute y- y(a,b,k,t) in the FONC and confirm that an identity in (a,b,k.t) results. (g) Confirm that for this specification of the model, the SOSC alone implies that output falls as the unit tax rises.

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