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- What is the difference between a fixed input and a variable input?Automobile manufacturing is an industry subject to significant economies of scale. Suppose there are four domestic auto manufacturers, but the demand for domestic autos is no more than 2.5 times the quantity produced at the bottom of the long-run average cost curve. What do you expect will happen to the domestic auto industry in the long run?For a firm with a Total Cost function TC C(Q), recall that the definitions of Marginal Cost (MC) and AverageTotal Cost (ATC) are given as follows:Marginal Cost (MC) = C'(0)Average Total Cost (ATC) = C(Q)/QProve that the marginal cost is equal to the average total cost (MC = ATC) when the average total cost is at itsminimum value.(Hint: By using the definition of average cost function, find the quantity that minimizes it by applying unconstraint optimization.Show that the FOC of the minimization problem implies that MC=ATC has to be satisfied at the minimum level of average cost.)
- Homework 2.1 Suppose a business manager of the factory wants to assess in terms of elasticity of demand, whetherthe products that his business is producing are complement goods or substitute goods inconsumption. So please explain which are the factors need to consider the long-run average cost curve in terms of usage of input?A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.