Assuming the market for chicken skewers is competitive. A typical firm selling

chicken skewers has the following short run cost functions.

TC$=100+40$q$-3($q$^2)+1/6($q$^3)$

MC$=40-6$q$+1/2($q$^2)$

a$.$ Find the amount of total fixed cost. $(1$ mark$)$

b$.$ Derive the average variable cost $($AVC$)$ function. Show your workings.

$(3$ marks$)$

c$.$ Find the output level that corresponds to the minimum AVC. Show your

workings. $($Hint: What is the feature of the minimum AVC curve?$)(3$ marks$)$

d$.$ Show the output level in part c$,$ MC curve and AVC curve in a well$-$labeled

diagram. $(3$ marks$)$

e$.$ Suppose that the market price of chicken skewers is $$40.$ Find the profitmaximizing output level for the typical firm in the short$-$run. Show your steps

clearly. $(3$ marks$)$

f$.$ Given the results of part e$,$ should the typical firm shut down? Explain your

answer clearly. $(4$ marks$)$

g$.$ Does the market for chicken skewers have a greater number of firms in the long

run than in the short run? Please provide a verbal explanation for your answer.

$(3$ marks$)$

Please answer the questions exactly.