Chapter $9$: Numerlcal Problems

Suppose rocking$-$chair manufacturing is a perfectly competitive industry in which there are $1,000$ identical firms. Each firm's total cost is related to output per day as follows:

$\backslash$table$[[$Quantity$,$Total Cost,$\backslash$table$[[$Total Variable$],[$Cost$]],\backslash$table$[[$Average Total$],[$Cost$]],$Marginal Cost$],[0,$$$500,,,],[1,1,000,,,],[2,1,300,,,],[3,1,500,,,],[4,1,800,,,],[5,2,200,,,],[6,2,700,,,],[7,3,300,,,],[8,4,400,,,]]$

a$.$ Complete the total variable cost, average total cost, and marginal cost columns in the table above.

b$.$ Plot the average total cost, average variable cost, and marginal cost curves for a single firm $($remember that values for marginal cost are plotted at the midpoint of the respective intervals$).$

c$,$ What is the firm's supply curve? How many chairs would the firm produce at prices of $$350,$ $$450,$$$550,$ and $$650?($In computing quantities, assume that a firm produces a certain number of completed chairs each day; it does not produce fractions of a chair on any one day. Round down to the nearest whole number.$)$

d$.$ Suppose the demand curve in the market for rocking chairs is given by the following table:

$\backslash$table$[[$Price$,$Quantlty Demanded$/$day$],[$$$650,5,000],[550,6,000],[450,7,000],[350,8,000]]$

Plot the market demand curve for chairs. Compute and plot the market supply curve, using the information you obtained for a single firm in part $($c$).$ What is the equilibrium price? The equilibrium quantity?

e$.$ Given your solution in part $($d$),$ plot the total revenue and total cost curves for a single firm. Does your graph correspond to your solution in part $($c$)?$ Explain