Question

3. Calculate conumer surplus and profit under a uniform price and under thirddegree price discrimination. Compare the two situations and comment on the result. Answer: Under uniform price, consumer surplus in each market is \[ \operatorname{CS}_{A}^{}=\frac{1}{2}\left(1-p^{}\right)^{2}=\frac{25}{128} \text { and } \quad \text { CS }_{i}^{}=\frac{1}{2}\left(\frac{1}{2}-p_{i}^{}\right)^{2}=\frac{1}{128} \] Hence, overall consumer surplus is \[ C S^{}=C S_{A}^{}+C S_{B}^{}=\frac{25}{128}+\frac{1}{128}=\frac{26}{128}=0.2 \] - With price discrimination, consumer surplus in each market is \[ C S_{A}^{}=\left(1-p_{A}^{}\right)^{2} / 2=\frac{1}{8} \text { and } C S_{B}^{\prime \prime}=\left(\frac{1}{2}-p_{B}^{ }\right)^{2} / 2=\frac{1}{32} \] Hence, overall cosnumer surplus is \[ C S^{ }=C S_{A}^{ }+C S_{a}^{ }=\frac{1}{8}+\frac{1}{32}=\frac{5}{32}=0.156 \] - Thus, under price discrimination consumer surplus is lower than with uniform price. Under aniform price, profit is \[ \pi^{}=p^{}\left(1-p^{}+1 / 2-p^{}\right)=\frac{9}{32}=0.28 \] With price discrimination, profit is \[ \pi^{ }=p_{A}^{ }\left(1-p_{A}^{}\right)+p_{B}^{}\left(1 / 2-p_{B}^{ *}\right)=\frac{5}{16}=0.31 \] Thus, under price discrimination profit is higher than with uniform price.

          3. Calculate conumer surplus and profit under a uniform price and under thirddegree price discrimination. Compare the two situations and comment on the result.

Answer:
Under uniform price, consumer surplus in each market is
\[
\operatorname{CS}_{A}^{*}=\frac{1}{2}\left(1-p^{*}\right)^{2}=\frac{25}{128} \text { and } \quad \text { CS }_{i}^{*}=\frac{1}{2}\left(\frac{1}{2}-p_{i}^{*}\right)^{2}=\frac{1}{128}
\]

Hence, overall consumer surplus is
\[
C S^{*}=C S_{A}^{*}+C S_{B}^{*}=\frac{25}{128}+\frac{1}{128}=\frac{26}{128}=0.2
\]
- With price discrimination, consumer surplus in each market is
\[
C S_{A}^{*}=\left(1-p_{A}^{*}\right)^{2} / 2=\frac{1}{8} \text { and } C S_{B}^{\prime \prime}=\left(\frac{1}{2}-p_{B}^{* *}\right)^{2} / 2=\frac{1}{32}
\]

Hence, overall cosnumer surplus is
\[
C S^{* *}=C S_{A}^{* *}+C S_{a}^{* *}=\frac{1}{8}+\frac{1}{32}=\frac{5}{32}=0.156
\]
- Thus, under price discrimination consumer surplus is lower than with uniform price.

Under aniform price, profit is
\[
\pi^{*}=p^{*}\left(1-p^{*}+1 / 2-p^{*}\right)=\frac{9}{32}=0.28
\]

With price discrimination, profit is
\[
\pi^{* *}=p_{A}^{* *}\left(1-p_{A}^{*}\right)+p_{B}^{*}\left(1 / 2-p_{B}^{* *}\right)=\frac{5}{16}=0.31
\]

Thus, under price discrimination profit is higher than with uniform price.

3. Calculate conumer surplus and profit under a uniform price and under thirddegree price discrimination. Compare the two situations and comment on the result.

Answer:
Under uniform price, consumer surplus in each market is

CSA^*=(1)/(2)(1-p^*)^2=(25)/(128) and CS i^*=(1)/(2)((1)/(2)-pi^*)^2=(1)/(128)

Hence, overall consumer surplus is

C S^*=C SA^*+C SB^*=(25)/(128)+(1)/(128)=(26)/(128)=0.2

- With price discrimination, consumer surplus in each market is

C SA^*=(1-pA^*)^2 / 2=(1)/(8) and C SB^''=((1)/(2)-pB^* *)^2 / 2=(1)/(32)

Hence, overall cosnumer surplus is

C S^* *=C SA^* *+C Sa^* *=(1)/(8)+(1)/(32)=(5)/(32)=0.156

- Thus, under price discrimination consumer surplus is lower than with uniform price.

Under aniform price, profit is

π^*=p^*(1-p^*+1 / 2-p^*)=(9)/(32)=0.28

With price discrimination, profit is

π^* *=pA^* *(1-pA^*)+pB^*(1 / 2-pB^* *)=(5)/(16)=0.31

Thus, under price discrimination profit is higher than with uniform price.

Added by Russell P.

Question

Please give Ace some feedback