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The derivation above shows the marginal rate of substitution which is the slope of the indifference curve. We make use of the total differential which is given by du in this case. Since the indifference curve represents indifference, it means total utility should not change such that du=0. Using that we calculate the slope of the indifference curve as Δy/Δx = – MUx/MUy. This means that the marginal rate of substitution (MRS) is given by the ratio of marginal utility of x (MUx) to the marginal utility of y (MUy).

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Recall that MUx is partial derivative of the utility function with respect to x. Our microeconomics tutor in London will focus on the basics of marginal rate of substitution and work with all the different types of preferences that can be tested at the undergraduate level.

Types of Preferences


Figure (a) shows typical convex preferences exhibited by Cobb-Douglas preferences. These preferences are for imperfect substitutes. The marginal rate of substitution is not constant, in fact, it diminishes as a consumer moves towards higher amounts of good x. This diminishing MRS is what makes imperfect substitutes convex in preferences.

Figure (b) shows perfect substitutes preferences which mean that the rate of substitution between two goods stays constant. These preferences imply that a consumer gives up exactly the same amount of good y for each unit of good x because x and y are perfectly substitutable.

Figure (c) shows perfect complements. These are goods that are consumed together in a fixed proportion and more of one good does not add to the utility without a proportional increase in the second good. For example, two slices of bread with a slice of cheese for a sandwich.

Our microeconomics tutors in London have extensive experience in preparing students for different types of indifference curves and consumer preferences. Constrained optimization using Lagrange works in the specific case when preferences are convex. For non-convex indifference curves, such as perfect substitutes, or perfect complements, or concave functions – we will teach students to look for corner solutions. Our tutors have a resource database of past exam papers and practice questions that will help students prepare for the exam.


Indifference Curves) For each of the following set of preferences sketch the indifference curves. Also explain whether the preferences satisfy weak monotonicity, strict monotonicity, weak convexity and strict convexity

  1. The two goods in the commodity space are plants and plant pots. The consumer will put 3 plants in every plant pot. They will not use plant pots with more or less than three plants. All they care about is the number of pots with three plants that they can make
  2. The two goods in the commodity space are cats and dogs. The consumer loves cats but hates dogs. Their preferences are determined by the number of cats minus the number of dogs (i.e. one bundle is preferred to another it has more cats minus the number of dogs
  3. The two goods in the commodity space are bananas for the consumer and bananas for the consumer s friend. The consumer is selfish, and all the consumer cares about in the number of bananas they have
  4. Now the consumer is a utilitarian. All they care about is the total number of bananas
  5. The two goods in the commodity space are chicken nuggets and fries. The consumer wants exactly 6 chicken nuggets and 50 fries, and all they care about is how close they are to this ideal bundle.

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