# Re-write each of the following statements in “if . then .” form. In each case identify the hypothesis(es) and the conclusion of the proposition.

4. Re-write each of the following statements in “if … then …” form.

In each case identify the hypothesis(es) and the conclusion of the proposition.

(a) He gets fat if he eats sugar, salt and transfat.

(b) When a firm is maximizing profit, MR=MC.

(c) Heavy rain all night will mean that the ground is wet in the morning.

(d) Black Caviar won the race and therefore had its nose in front at the post.

(e) Black Caviar won the race and therefore was first out of the barrier.

(f) I am now twenty one years of age, so I must have been twenty at some

stage.

Comment on whether the hypothesis(es) is/are necessary, sufficient, necessary and

sufficient or none of these, for the conclusion.

5(i). Define the converse of a proposition.

5(ii) Is the converse of a true statement necessarily true? Why?

5(iii) Write down the converse of 4(b) and 4(f). Are these statements true? Why?

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*6. (Silberberg): Suppose revenue ????(????) from the sale of ???? units of a good by a firm

is given by ????(????) = ln⁡(????) and the total cost ????(????) of producing ???? units of the good is

given by ????(????) = ???????? with ???? > 0⁡for⁡???? ≥ 1.

(a) Write down an expression for the profit function for this firm and draw its graph.

(b) Calculate the supply of ???? as a function of ????, assuming that the firm chooses its

output level in order to maximize profit.

(c) Work out the sign of the effect of a change in ???? on ???? by exploiting a second order

necessary condition for profit maximization.

(d) Interpret this result economically.

7. Obtain a balloon. Flatten the balloon out on a table and using a soft-tipped pen and

rule, draw a triangle on the balloon. Now inflate the balloon. What is the sum of the

interior angles, relative to 1800

? What point(s) about theorizing in economics does

this illustrate?

*8. Tutorial Reading 1. Read and then summarise: Birendra K. Rai, Chiu Ki So, and

Aaron Nicholas (2012), “A primer on mathematical modelling in economics”, Journal

of Economic Surveys, Vol. 26, No. 4, pp. 594 – 95 and stop at the heading: ‘2. The Tool:

R’.

Debreu model of general equilibrium”, (in) The New Palgrave Dictionary of

Economics, Second Edition, 2008, Edited by S. N. Durlauf and L.E. Blume, starting at

*9. Listen to/view and then summarise:

Go to https://www.youtube.com/watch?v=a20OW3hl1ow and summarize from

20:00mins to 24:00mins. Explain what the remarks made here have to do with

‘Scientific Method’.

10. Explain the meaning and significance for economic theory of the following

statement: “There is no such thing as a condition free theorem”.