Question

1.The first-order derivative of a function of the form y=f(x) evaluated at x=2 is:

	a.	The rate of change [Delta_y/Delta_x], where Delta_x=3-2 and Delta_y=f(3)-f(2).
	b.	The slope of the line that is tangent to y=f(x) at the point (2,f(2)) in the (x,y) Cartesian space.
	c.	The slope of the line that is tangent to y=f’(x) at the point (2,f’(2)) in the (x,y’) Cartesian space.
	d.	None of the above.

2.A university hires you to advise them on how to maximise the revenue they raise from staff parking fees. You know that the staff demand for parking is: X = 2,000 –2p, where X: number of staff buying annual parking, p: annual parking fee. To maximise revenue, the university should set the fee at:

	a.	p=1,000 $/year.
	b.	p=800 $/year.
	c.	p=400 $/year.
	d.	p=500 $/year.

3.According to microeconomic theory, an input factor may be:

	a.	Fixed in the short run, but will always be variable in the long run.
	b.	Fixed in the short run, and fixed or variable in the long run.
	c.	Variable in the short run, but will always fixed in the long run.
	d.	Either fixed or flexible in the short run, and either fixed or flexible in the long run.

4.In the profit maximisation model covered in Varian (2014, Ch. 20), an isoprofit curve is:

	a.	The locus of output (y) and variable input x_1 associated with a same cost level.
	b.	The locus of variable input x_1 and variable input x_2 associated with a same profit level.
	c.	The locus of output (y) and variable input x_1 associated with a same profit level.
	d.	All of the above.

5. Which of the following is NOT an assumption of perfect competition:

	a.	There are no barriers to entry.
	b.	All firms have access to the same technology and input factors.
	c.	All firms pay the same price for input factors (and if quantity discounts apply, all firms buying the same input quantity face the same price).
	d.	Firms try to push competitors out of the market by setting the price of the product they sells at a level that is lower than the competitors’ price.
	e.	There are no barriers to exit.
	f.	Consumers are small in the sense that they cannot individually affect the market, so they behave as price-takers.

Answer 1

1) b) slope of the line that is tangent to y=f(x) at point (2,f(2)) in the (x,y) cartesian space.

2)Demand

X= 2000-2p

maximize revenue

Revenue = P*X

= (2000-2p)p

Maximize it we differentiate with respect to p , we get

2000- 4p =0

p= 500

hence , d) $ 500 per year.

3)a) Fixed in the short run, but will always be variable in the long run.

example can be capital.

4)b)The locus of variable input x_1 and variable input x_2 associated with a same profit level.

5) d) Firms try to push competitors out of the market by setting the price of the product they sells at a level that is lower than the competitors’ price.