1. One question from the fi question cluster and:
   • Let f (x1, x2) = 2x0.5x0.25be a production Find the short

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run average cost curve for each of x2  = 1, 1.5, 2, 2.5, 3 and for generic prices w1, w2. Find the marginal cost curve as well. Find the long run average cost curve for specific prices of w1 = w2 = 1. Graph your results. Be sure to include (and label) in your graph the levels of output for which the long run average cost curve would coincide with each of the short run curves above (for the specific prices). Find the long run marginal cost curve at these levels.

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• Let c(y1, y2)  =  y1  + y2  + (y1y2) 3     Does  this  cost  function  have economies of scale for y1? What about economies of scope for any strictly positive y1 and y2. Hint, economies of scope exist if for a positive set of y1 and y2, c(y1, y2) > c(y1, 0) + c(0, y2)

• Let y = Axα. Suppose that we see when p = 2, w = 1 and y = 8 and when p = 1, w = 0.2, and y = Can we identify the parameters of the production function from just this information? Infer what x must be from the above and graph what an economist who didn’t know the production function but could see α would know about the production set.
• Suppose a Cobb Douglass production function with two inputs and exponents inside the production function y = xα1 xα2  that are

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less than one. Derive the profi maximizing choices of x1, x2, and y for arbitrary prices. How does this simply if α1  and α2  sum up to one?

• Let AC(y) = 1/y + 2 + 0.1y. Find the efficient point of production for this fi Suppose every fi in the industry has access to the technology, find the region of economies of scope, e. the amount of output where production is cheaper if it is concentrated in one fi  Derive the long run, industry, average cost for this function if production is undertaken by the most cost efficient number of fi      for each level of output.
• Assume a market demand function of D(P ) = 100 − P and a per fi cost function of C(q) or 20q. Find the competitive equilib- Assume that in order to boost wages, the local govt applies a minimum price on output of 30. Assume, in the fi case, that there is an entry restriction so that a monopolist will fi all of the demand at the regulated price fl or. What are the effect of this on output? Suppose instead that the regulation raises the cost of the product to achieve the same price so that C(q) = 20q + R¯q. (In this case either the regulation imposes a cost due to suboptimal restrictions on input uses or there is no additional entry regulation so that profi seeking fi bid the price of inputs upwards.) Go back to the fi part of the analysis with the regulated price but not the unavoidable per unit additional cost. Suppose there is an innovation which can lower the cost of providing the good to 5q. What is the value of this innovation under unregulated market to consumers, producers and society as a whole (total surplus)? [Note you are looking at the change in these types of surpluses af- ter innovation not the level.] What is the value of this innovation under a market with both price and entry regulations but no cost infl regulations? How does this type of price control affect incentives to innovate?
• Repeat the above with the higher regulatory driven costs but as- sume that in addition the innovation does not affect R¯ so that it is likely a regulatory How does the value of an innovation compare to the two cases above? Note, in terms of interpretation, that if R¯ is fi at the level found above the price control won’t bind in the marketplace. Thus this can be a policy that produces higher prices without strict enforcement of a price control. But after the innovation without a price control, the price of output will fall. Repeat the above with the same value of R¯ but no price regulation.  Under which set of policies are regulations the most valuable either to society or to producers?

• Use profi and revealed choices by fi  to show the law of Be sure to defi what is meant by the law of supply? How would the above result change if a fi  faced a cost of (q1 − q2)2 if it changed output from q1 to q2 after a price change.
• Assume an  isoquant  for  a  fi         level  of  output  equal  to  y¯  =

1      1

1/2x 2 x 3

Fix w1  = 1.  Show how the cost  minimizing bundle

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changes as w2  moves from 1 to 2.  You can graph x1  and x2  on separate graphs as a function of w.

• Provide a historical situation in which periods of low infl  can be used to estimate the effect of usury laws (a price ceiling on interest rates) for similar values of real interest rates without low infl      How do mortgage lenders typically ration credit when price ceilings bind?
• Lets suppose that a fi owns a proven oil reserve of k units which cannot be transferred and a technology for producing oil from

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reserves of y = k 3 .   You own a fi         amount  of  non-resaleable reserves k¯.  Suppose the price of oil is constant the interest rate (1+r)=1.03 and the oil expires after 2 periods.  Solve for efficient use of oil over two periods. Suppose that an outside policy maker wants to reduce current oil production.  Can they do that with a constant tax on oil production?  What must be true of any of tax profi       which accomplishes the policy makers goal?  [A tax profi is a set of time specific marginal tax rates.]  Suppose instead the

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production  function equals y = k 3   − 1 for any y > 0 but is equal to zero for no production.    How do your answers to the above change?

• Suppose there is an industry with fi costs equal to 1 and an average variable cost equal to 5 + 0.1y. Suppose that price in this industry equals 10 and is determined using competitive Find the amount of production and the producer surplus (short run). Be sure to define producer surplus and show it graphically. Find also the short run and long run break even prices for a fi that may face a rival capable of large scale and very quick en- try.  Suppose demand is sufficiently large, What is the long run equilibrium price for this industry?

• Assume the previous industry is such that there is an incumbent fi which cannot recover the (already paid) fixed cost over any horizon even if it exits the industry but fi  that want to enter still must pay What is the long run equilibrium price and distribution of profits for this industry?
• Derive the isoquant for a fi that has two inputs which are perfect complimen Use this to solve for the fi cost minimizing input bundle and in terms the cost function c(y). Repeat for a fi that has a perfect substitute technology for producing output. You should be able to due this for any preferences within these classes and your answer should have a specific, though not-necessarily, polynomial analytical form.
• Given our discussion in class about eyeglasses and correcting for any typos in the slide, we can speculate about another similar historical even In 1977, the Supreme Court ruled that indi- vidual states could not ban lawyers from advertising either their availability or their prices. Unlike with eyeglasses, all states had previously enacted a ban. What do you think was the effect of this decision on (long run) legal fees?