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EC1A1 课程简介
Teacher responsible
Prof Dimitra Petropoulou 32L 4.27
Availability
This course is compulsory on the BSc in Econometrics and Mathematical Economics and BSc in Economics. This course is not available as an outside option nor to General Course students.
Pre-requisites
Students must have completed Economics (EC1P1) and Elementary Statistical Theory I (ST109).
Students must also either have completed Quantitative Methods (Mathematics) (MA107) or else be taking Mathematical Methods (MA100) alongside.
Prerequisites
Course content
This course introduces students to the principles of microeconomics analysis, including recent developments in thinking around decision-making. The first part of the course explores consumer rationality and decision-making under constraints and under uncertainty, including selected applications to savings and labour supply decisions. Students will also be introduced to behavioural economics and insights from psychology relating to consumer decisions. The second part of the course explores firm decision-making in different market structures. Insights from consumer and producer theory will be combined with evidence to address important policy-relevant questions and explore the role of government policy.
EC1A1 Microeconomics HELP（EXAM HELP， ONLINE TUTOR）
Consider a person that spends all his fixed income $\mathrm{M}$ on two goods. Currently he spends one third of the income on good 2. If the price of good one rises by $50 \%$ and consumer’s income by one third, what is the change in the consumer’s welfare?
Let $p_1$ and $p_2$ be the prices of goods 1 and 2 respectively, and let $x_1$ and $x_2$ be the quantities of goods 1 and 2 respectively that the person consumes.
We are given that the person spends all their fixed income $M$ on the two goods, so we have the budget constraint:
$$
p_1 x_1+p_2 x_2=M
$$
We are also given that the person currently spends one third of their income on good 2, so we have:
$$
p_2 x_2=\frac{1}{3} M
$$
Dividing the second equation by the first equation, we get:
$$
\frac{p_2}{p 1} \cdot \frac{x_2}{x_1}=\frac{1}{3} \cdot \frac{1}{M}
$$
Now suppose that the price of good 1 increases by $50 \%$ to $\$ 1.5 p_{-} 1 \$$, and the person’s income increases by one third to $\$ \backslash f r a c{4}{3} M \$$. The new budget constraint becomes:
$$
\left(1.5 p_1\right) x_1+p_2 x_2=\frac{4}{3} M
$$
We can solve for $\$ x_{-} 1 \$$ in terms of $\$ x_{-} 2 \$$ using the second equation above:
$$
x_1=\frac{1}{p_1}\left(\frac{1}{3} M-p_2 x_2\right)
$$
Substituting this expression for $\$ x_{-} 1 \$$ into the new budget constraint, we get:
$$
\frac{3}{2} p_2 x_2+p_2 x_2=\frac{4}{3} M-\frac{1}{p_1}\left(\frac{1}{3} M-p_2 x_2\right)
$$
Simplifying this expression, we get:
$$
\left(\frac{3}{2} p_2+p_2\right) x_2=\frac{4}{3} M-\frac{1}{3 p 1} M
$$
which gives us:
$$
x_2=\frac{\frac{4}{3} M \frac{1}{3 p 1} M}{\frac{5}{2} p 2}
$$
Similarly, we can solve for $\$ x_{-} 1 \$$ using the first equation above:
$$
x_1=\frac{1}{p_1}\left(\frac{4}{3} M-\frac{5}{2} p_2 x_2\right)
$$
Substituting the expression for $\$ x_{-} 2 \$$ that we found above, we get:
$$
x_1=\frac{1}{p_1}\left(\frac{4}{3} M-\frac{5}{2} p_2 \cdot \frac{\frac{4}{3} M \frac{1}{3 p_1} M}{\frac{5}{2} p_2}\right)
$$
Simplifying this expression, we get:
$$
x_1=\frac{2}{3} M-\frac{4}{15} \frac{M}{p_1}
$$
Now we can calculate the consumer’s welfare before and after the price and income changes. The consumer’s utility function is not specified, so we cannot calculate the exact level of welfare, but we can use the fact that the consumer is spending all their income on the two goods to argue that the consumer is on their budget constraint.
During a war, food (good 1) and clothing (good 2) are rationed. In addition to a money price, $p_i(\mathrm{i}=1,2)$, a certain number of ration coupons $q_i$ must be paid to obtain good i. Each consumer has an allocation of ration coupons $\mathrm{Q}$ (coupons are infinitely divisible) which may be used to purchase either good, and also has a fixed income $M$.
(a) Illustrate the budget set. Explain carefully.
(b) Suppose the money income of a consumer is raised and he buys more food and less clothing. It follows that clothing is an inferior good. True or false?
(a) The budget set consists of all the combinations of food and clothing that a consumer can purchase with their income and ration coupons. Let $\$ x_{-} 1 \$$ and $\$ x_{-} 2 \$$ be the quantities of food and clothing, respectively, that the consumer purchases. Then the budget constraint is:
$$
p_1 x_1+q_1 x_1+2 q_2 x_2+p_2 x_2+q_1 x_2 \leq M+Q\left(q_1+q_2\right)
$$
The left-hand side of the inequality represents the total cost of the consumer’s purchases, which includes the money price of each good multiplied by the quantity purchased, as well as the number of ration coupons required for each good multiplied by the quantity purchased. The right-hand side represents the total resources available to the consumer, which includes their income and the allocation of ration coupons.
(b) False. If the consumer buys more food and less clothing as their income increases, this implies that food is a normal good and clothing is an inferior good.
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