1)In a monopoly, is P always greater than MR? 2)Due to price discrimination of second and third degree, social welfare is reduced since it creates deadweight loss

1)please see the attached file.

2)Third Degree Price Discrimination:

If the monopoly can separate its buyers into relatively few identifiable markets (such as rural - urban, domestic- foreign, prime time - off prime and pursue a separate monopoly pricing policy in each market, this is called third degree price discrimination. Knowledge of the price elasticities of demand in these markets is sufficient to pursue such a policy. The monopoly then sets a price in each market according to the inverse elasticity rule. Assuming that marginal cost is the same in all markets, the result is a pricing policy in which:

[Math Processing Error]Pi(1+1ηi)=Pj(1+1ηj), or

[Math Processing Error]PiPj=1+1ηj1+1ηi

The welfare consequences of third-degree price discrimination are, in principle, ambiguous. Relative to a single-price policy,the discriminating policy requires raising the price in the less elastic market and reducing it in the more elastic one. Hence, the changes have an offsetting effect on total allocational losses.

Second Degree Price Discrimination:

It occurs whenever a firm charges its consumers different prices depending on the quantity of goods or services they use.Both the deadweight loss as well as the consumer surplus are positive under third-degree price discrimination while they both can be zero under second-degree price discrimination and the social surplus is maximum