Please explain how to do these -
1) Consider two consumers with following demand functions -
X = 50 - p
X = 100 -2p
The marginal cost of production is 6. Calculate the equilibrium consumption levels of the consumers if
(i) the good is private
(ii) the good is a public
2) Suppose you want to measure consumer's welfare due to price change through consumer surplus. this can be done for -
(i) cobb-douglas utility function
(ii) leontief utility function
(iii) quasi-linear utility function
(iv)all of the above
3) Suppose a monopoly is forced to charge the same price in two markets with the following demand curves: Q1 = 20 - P1 and Q2 = 10 - P2 . The marginal cost of production is c>0. What price does it charge?
4) Consider a monopoly with market demand function D(p) = a -p The cost function is C(q) = cq. We assume 0<c<a. Compare the monopoly output in the two situations:
(i) monopoly subject to specific tax rate of t
(ii) monopoly subject to advalorem tax rate of t
Which one is more desirable from social point of view?
5) Find the domain of the following function:
F(xy) = (x+y)/(y^2 - 4x^2)
6) Is this function always continuous and differentiable?
f(z) = mod(z-6) - 3
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